{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CIMHGPQSYWPGFGRFU6GJO7ZUBB","short_pith_number":"pith:CIMHGPQS","canonical_record":{"source":{"id":"1203.5591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-26T07:23:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e690edea70db863b2e67440a7e76ee22dcb876210e5c1f5b8146070a2f0f0d0f","abstract_canon_sha256":"4c9bec1b6c85c0ac6268731123deda88aa90b3af9a9d2821021d136ba56dbd39"},"schema_version":"1.0"},"canonical_sha256":"1218733e12c59e629a25a78c977f34087ddde17d607c94e57f2a75255be30d12","source":{"kind":"arxiv","id":"1203.5591","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5591","created_at":"2026-05-18T03:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5591v2","created_at":"2026-05-18T03:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5591","created_at":"2026-05-18T03:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"CIMHGPQSYWPG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CIMHGPQSYWPGFGRF","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CIMHGPQS","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CIMHGPQSYWPGFGRFU6GJO7ZUBB","target":"record","payload":{"canonical_record":{"source":{"id":"1203.5591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-26T07:23:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e690edea70db863b2e67440a7e76ee22dcb876210e5c1f5b8146070a2f0f0d0f","abstract_canon_sha256":"4c9bec1b6c85c0ac6268731123deda88aa90b3af9a9d2821021d136ba56dbd39"},"schema_version":"1.0"},"canonical_sha256":"1218733e12c59e629a25a78c977f34087ddde17d607c94e57f2a75255be30d12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:59.807521Z","signature_b64":"HaSVS59eJ/w+P0J6PgpAxkABGzFk1d9WCaoQtZmUkafrpMSXMtcaYsNiWrynCeAKxmU1V8+wGPk3juOzBcfUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1218733e12c59e629a25a78c977f34087ddde17d607c94e57f2a75255be30d12","last_reissued_at":"2026-05-18T03:33:59.806821Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:59.806821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.5591","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XTE+bkzVT/fwqYG2uWpUpWiik1lcTlyGzJ32a+eyJqqN7NHPrOaM/RCDQhPD1pIs8MFoxgMVlaPdBbNIxe9UBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:18:11.677835Z"},"content_sha256":"8bb4b3140de358b6b2963c23be7cda8777a3494dad414a9a55035350ac5e4600","schema_version":"1.0","event_id":"sha256:8bb4b3140de358b6b2963c23be7cda8777a3494dad414a9a55035350ac5e4600"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CIMHGPQSYWPGFGRFU6GJO7ZUBB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cutting the same fraction of several measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Arseniy Akopyan, Roman Karasev","submitted_at":"2012-03-26T07:23:51Z","abstract_excerpt":"We study some measure partition problems: Cut the same positive fraction of $d+1$ measures in $\\mathbb R^d$ with a hyperplane or find a convex subset of $\\mathbb R^d$ on which $d+1$ given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5591","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uum4UW3M2XhRs+ZnOm24Ndmr2/eYWmmUfm81NPNx7nsi48O+zvPRno+BfpvByENNpwTQEDxDnRvRRaWZjb3sAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:18:11.678555Z"},"content_sha256":"f273fe8658d13e94a6980cc133a47539b365a9c133d37b623fc9e5cfbf691e2b","schema_version":"1.0","event_id":"sha256:f273fe8658d13e94a6980cc133a47539b365a9c133d37b623fc9e5cfbf691e2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CIMHGPQSYWPGFGRFU6GJO7ZUBB/bundle.json","state_url":"https://pith.science/pith/CIMHGPQSYWPGFGRFU6GJO7ZUBB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CIMHGPQSYWPGFGRFU6GJO7ZUBB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T14:18:11Z","links":{"resolver":"https://pith.science/pith/CIMHGPQSYWPGFGRFU6GJO7ZUBB","bundle":"https://pith.science/pith/CIMHGPQSYWPGFGRFU6GJO7ZUBB/bundle.json","state":"https://pith.science/pith/CIMHGPQSYWPGFGRFU6GJO7ZUBB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CIMHGPQSYWPGFGRFU6GJO7ZUBB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CIMHGPQSYWPGFGRFU6GJO7ZUBB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4c9bec1b6c85c0ac6268731123deda88aa90b3af9a9d2821021d136ba56dbd39","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-26T07:23:51Z","title_canon_sha256":"e690edea70db863b2e67440a7e76ee22dcb876210e5c1f5b8146070a2f0f0d0f"},"schema_version":"1.0","source":{"id":"1203.5591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5591","created_at":"2026-05-18T03:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5591v2","created_at":"2026-05-18T03:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5591","created_at":"2026-05-18T03:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"CIMHGPQSYWPG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CIMHGPQSYWPGFGRF","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CIMHGPQS","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:f273fe8658d13e94a6980cc133a47539b365a9c133d37b623fc9e5cfbf691e2b","target":"graph","created_at":"2026-05-18T03:33:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study some measure partition problems: Cut the same positive fraction of $d+1$ measures in $\\mathbb R^d$ with a hyperplane or find a convex subset of $\\mathbb R^d$ on which $d+1$ given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions.","authors_text":"Arseniy Akopyan, Roman Karasev","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-26T07:23:51Z","title":"Cutting the same fraction of several measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5591","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8bb4b3140de358b6b2963c23be7cda8777a3494dad414a9a55035350ac5e4600","target":"record","created_at":"2026-05-18T03:33:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4c9bec1b6c85c0ac6268731123deda88aa90b3af9a9d2821021d136ba56dbd39","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-26T07:23:51Z","title_canon_sha256":"e690edea70db863b2e67440a7e76ee22dcb876210e5c1f5b8146070a2f0f0d0f"},"schema_version":"1.0","source":{"id":"1203.5591","kind":"arxiv","version":2}},"canonical_sha256":"1218733e12c59e629a25a78c977f34087ddde17d607c94e57f2a75255be30d12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1218733e12c59e629a25a78c977f34087ddde17d607c94e57f2a75255be30d12","first_computed_at":"2026-05-18T03:33:59.806821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:59.806821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HaSVS59eJ/w+P0J6PgpAxkABGzFk1d9WCaoQtZmUkafrpMSXMtcaYsNiWrynCeAKxmU1V8+wGPk3juOzBcfUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:59.807521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bb4b3140de358b6b2963c23be7cda8777a3494dad414a9a55035350ac5e4600","sha256:f273fe8658d13e94a6980cc133a47539b365a9c133d37b623fc9e5cfbf691e2b"],"state_sha256":"d84ec77da97c115c0abee7ee18f8365b7c02dda8927c8e9b048b356588834ba0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RNvaE+q4XLEzAPpQf9eU6fBOoiQaxNCoAsefS09dN+QWULFkKLpbHKZfPAKfTD+PrrzOlWRA7R2+y5U7hSFNCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T14:18:11.681998Z","bundle_sha256":"a20af85cb8e82675224a399fdde4b8a4cb6e1bc9451b9e7a11e7ea3afd15b5d0"}}